An object, previously at rest, slides #15 m# down a ramp, with an incline of #pi/3 #, and then slides horizontally on the floor for another #12 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

#mu=(5sqrt3)/13#

#E_A=m*g*h#
#"Work Doing by The Friction Force Along AB:"#
#W_"AB"=mu*m*g*cos (pi/3)*15#
#"Work Doing by The Friction Force Along BD:"#
#W_"BD" =mu*m*g*12#
#E_A=W_"AB" +W_"BD"#
#cancel(m*g)*h=mu*cancel(m*g)*cos(pi/3)*15+mu*cancel(m*g)*12#
#h=mu*15*cos(pi/3)+mu*12*#
#alpha=pi/3#
#h=15*sin(pi/3)#
#15*sin(pi/3)=mu(15*cos(pi/3)+12)#
#15*sqrt3/2=mu(15*1/2+12)#
#7,5sqrt3=mu(39/2)#
#15sqrt3=mu*39#
#mu=(15sqrt3)/39#
#mu=(5sqrt3)/13#

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Answer 2

Isabella Alvarez

The kinetic friction coefficient of the material is approximately 0.225.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.